Abstract
We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of undefinability results. Second, we treat relativized common knowledge, underlining how the same results still hold for a different modality in a different semantics. Third, we show the flexibility of the approach by generalizing it to multi-agent systems, encompassing the case of multi-agent plausibility models.
Original language | English |
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Pages (from-to) | 1-33 |
Number of pages | 33 |
Journal | Studia Logica |
Volume | 106 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2018 |
Keywords
- Bisimulation
- Conditional logic
- Modal logic